Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

public class P192A {

  public PrintWriter run() {
    int n = sc.nextInt() * 2;

    for (int h = (int)Math.sqrt((double)n); h >= 1; h--) {
      int hRes = h * (h + 1);
      for (int l = (int)Math.sqrt((double)n - hRes); l >= 1; l--) {
        int res = l * (l + 1) + hRes;
        if (res == n) {
          pw.println("YES");
          return pw;
        }
        if (res < n) {
          break;
        }
      }
    }

    pw.println("NO");
    return pw;
  }

  private Scanner sc = new Scanner(new BufferedInputStream(System.in));
  private PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));

  public static void main(String[] args) throws Exception {
    new P192A().run().close();
  }
}